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Scope and Sequence AM™ CC Geometry Library The Accelerated Math™ scope and sequence is based on extensive mathematics and standards research and consultation from mathematics educators, mathematicians, and university researchers. You're sure to find objectives that reinforce the skills you are teaching, regardless of what instructional materials you use. Accelerated Math makes it easy to select and organize objectives to suit your textbook and your own teaching approach. This Accelerated Math library provides the following scope and sequence of objectives Topic 1 - Congruence, Proof, and Constructions • • • • • • • • Identify a function that describes a transformation Determine the graph of a transformation given a function that describes the translation Determine the rotations or reflections that carry a rectangle, parallelogram, trapezoid, or regular polygon onto itself Determine the coordinates of the image of a figure's vertex after two transformations of the same type Determine the coordinates of the image of a figure's vertex after two transformations of different types Determine a sequence of transformations that will carry a given figure onto another figure Identify corresponding parts of congruent triangles in terms of rigid motion Solve a problem using inequalities in a triangle Topic 2 - Similarity, Proof, and Trigonometry • • • • • Identify similar triangles using triangle similarity postulates or theorems Determine the length of a side or the measure of an angle given two similar triangles and numeric values for side lengths or angle measure Determine the length of a side or the measure of an angle given two similar triangles and algebraic expressions for side lengths or angle measures Determine a length in a triangle using a midsegment and given numeric values for lengths Determine a length in a triangle using a midsegment and given algebraic expressions for lengths • • • • • • • • • • • • • • • Determine a length in a triangle using parallel lines and proportional parts Determine a length given the perimeters of similar triangles or the lengths of corresponding interior line segments Determine a length using similar triangles formed by the altitude to the hypotenuse of a right triangle WP: Determine a length in a triangle using similarity Complete a proof using congruence and similarity theorems Determine a length using the properties of a 45-45-90 degree triangle or a 30-60-90 degree triangle WP: Determine a length using the properties of a 45-45-90 degree triangle or a 30-60-90 degree triangle Solve a multi-step problem using the properties of a 45-45-90 degree triangle and/or a 30-60-90 degree triangle Determine a sine, cosine, or tangent ratio in a right triangle Determine a length using a sine, cosine, or tangent ratio in a right triangle Determine the measure of an angle using a sine, cosine, or tangent ratio in a right triangle Solve a problem using the Pythagorean theorem and a sine, cosine, or tangent ratio in a right triangle WP: Solve a problem involving a complex figure using the Pythagorean theorem WP: Determine a length in a right triangle using a sine, cosine, or tangent ratio WP: Determine the measure of an angle in a right triangle using a sine, cosine, or tangent ratio P.O. Box 8036|Wisconsin Rapids, WI 54495-8036|(800) 338-4204|www.renlearn.com © 2014 Renaissance Learning, Inc. All rights reserved. Page 1 of 4 R56475.140114 Scope and Sequence • • • • • • Determine the area of an oblique triangle Solve a problem using the law of sines for non-ambiguous cases (ASA and AAS) Solve a problem using the law of sines for the ambiguous case (SSA) Solve a problem using the law of cosines WP: Solve a problem using the law of sines or the law of cosines WP: Solve a problem involving density and area Topic 3 - Extending to Three Dimensions • • • • • • • • • Determine the volume of a right pyramid or a right cone Determine a measurement given the volume of a right pyramid or a right cone WP: Determine a measurement given the volume of a right pyramid or a right cone Determine a measurement given the volume of a sphere WP: Determine a measurement given the volume of a sphere WP: Solve a problem involving the volume of a complex solid figure WP: Solve a problem involving density and volume Determine the shape of a 2dimensional cross section of a 3dimensional object Identify the 3-dimensional object generated by a rotation of a 2dimensional object Topic 4 - Connecting Algebra and Geometry Through Coordinates • • Determine whether lines through points with given coordinates are parallel or perpendicular Determine the coordinates of a point through which a line must pass in order to be parallel or perpendicular to a given line AM™ CC Geometry Library • • • • • • • • • • Determine whether two lines are perpendicular or parallel given the equations of the lines Determine an equation of a line in slope-intercept form that goes through a given point and is parallel or perpendicular to a given line Determine an equation of a line in standard form that goes through a given point and is parallel or perpendicular to a given line Determine the midpoint of a line segment given the coordinates of the endpoints Solve a problem involving the midpoint formula Determine the point on a line segment that divides the segment into a given ratio Determine the perimeter of a polygon given the coordinates of the vertices of the figure Determine the area of a right triangle or a rectangle given the coordinates of the vertices of the figure Derive the equation of a vertically oriented parabola given a focus and a directrix Derive the equation of a horizontally oriented parabola given a focus and a directrix Topic 5 - Circles With and Without Coordinates • • • • • • • Determine the length of a line segment, the measure of an angle, or the measure of an arc given a tangent to a circle Determine a length using the relationship between chords and radii Determine the measure of an arc or an angle using properties of an inscribed triangle or quadrilateral Determine the measure of an angle using the relationship between inscribed angles, circumscribed angles, and/or central angles Determine the length of an arc Determine the area of a sector of a circle Determine an equation of a circle P.O. Box 8036|Wisconsin Rapids, WI 54495-8036|(800) 338-4204|www.renlearn.com © 2014 Renaissance Learning, Inc. All rights reserved. Page 2 of 4 R56475.140114 Scope and Sequence • • Determine the radius or center of a circle given an equation Complete the square to determine the center or radius of a circle given the equation Topic 6 - Applications of Probability • • • • • Determine the probability of independent events Represent data using a two-way frequency table Approximate conditional probabilities using a two-way table as a sample space Determine the conditional probability of an event A given an event B Determine the probability of an event using the addition rule of probability, P(A or B) = P(A) + P(B) - P(A and B) AM™ CC Geometry Library • • • • • • • • Determine the probability of an event using the multiplication rule of probability, P(A and B) = P(A)P(B|A) = P(B)P(A|B) WP: Determine the number of permutations possible in a given situation Determine a probability using permutations WP: Solve a probability problem involving permutations WP: Determine the number of combinations possible in a given situation Determine a probability using combinations WP: Solve a probability problem involving combinations Analyze a decision or a strategy using simple probability concepts P.O. Box 8036|Wisconsin Rapids, WI 54495-8036|(800) 338-4204|www.renlearn.com © 2014 Renaissance Learning, Inc. All rights reserved. Page 3 of 4 R56475.140114 Scope and Sequence Accelerated Math Libraries include an almost unlimited supply of dynamic algorithm-generated problems for both assisted-response (multiplechoice) and free-response assignments. Twenty libraries are available: Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 Algebra 1 Algebra 2 Geometry Math 1 Math 2 Math 3 Probability & Statistics Pre-Calculus Calculus Financial Literacy Math 1 Financial Literacy Math 2 AM™ CC Geometry Library Please call us toll-free at 1-800-338-4204 to order this Accelerated Math library or to request the Scope and Sequence for other libraries. Accelerated Math Library AM CC Geometry Library P.O. Box 8036|Wisconsin Rapids, WI 54495-8036|(800) 338-4204|www.renlearn.com © 2014 Renaissance Learning, Inc. All rights reserved. Page 4 of 4 R56475.140114